Finite Group DatabasebetaFinite Group DatabasebetaOrder 1984.
426 conjugacy classes of subgroups; only the 183 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 183 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×C4×C31 | C2 | semidirect |
| 3. C22×C4×D31 | C2 | semidirect |
| 4. C2×C22⋊Dic31 | C2 | semidirect |
| 5. C4×C22⋊D31 | C2 | direct (N × H) |
| 6. C2×(C2×D31)⋊C4 | C2 | semidirect |
| 7. C2×Dic31⋊C4 | C2 | semidirect |
| 8. C2×C4×Dic31 | C2 | semidirect |
| 14. C22×C4×C31 | C22 | semidirect |
| 15. C2×C22⋊D31 | C4 | direct (N × H) |
| 21. C2×C4×D31 | C22 | semidirect |
| 22. C22⋊Dic31 | C22 | semidirect |
| 23. (C2×D31)⋊C4 | C22 | semidirect |
| 24. Dic31⋊C4 | C22 | semidirect |
| 25. C4×Dic31 | C22 | semidirect |
| 28. C23×C31 | C2×C4 | semidirect |
| 33. C22×D31 | C2×C4 | semidirect |
| 37. C2×C4×C31 | D4 | semidirect |
| 40. C22⋊D31 | C2×C4 | direct (N × H) |
| 43. C2×Dic31 | C2×C4 | semidirect |
| 52. C22×C31 | C22×C4 | semidirect |
| 59. C2×D31 | C22×C4 | semidirect |
| 61. C4×C31 | C2×D4 | semidirect |
| 64. Dic31 | C22×C4 | semidirect |
| 67. C2×C31 | C4×D4 | semidirect |
| 74. C23×C4 | D31 | semidirect |
| 80. C31 | C2×C4×D4 | semidirect |
| 93. C22×C4 | C2×D31 | semidirect |
| 104. C23 | C4×D31 | semidirect |
| 117. C2×C4 | C22⋊D31 | direct (N × H) |
| 128. C22 | C2×C4×D31 | semidirect |
| 136. C4 | C2×C22⋊D31 | direct (N × H) |
| 139. C2 | C4×C22⋊D31 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4×C31 | 2 |
| C22×C22⋊D31 | 2 |
| C22×C4×D31 | 2 |
| C2×C22⋊Dic31 | 2 |
| C4×C22⋊D31 | 2 |
| C2×(C2×D31)⋊C4 | 2 |
| C2×Dic31⋊C4 | 2 |
| C2×C4×Dic31 | 2 |
| C2×C4×D4 | 31 |